How can I check the chosen preset in Python?
That's not possible in Blender's current preset system implementation. 

Plain preset execution operator, script.execute_preset, merely executes the script file corresponding to selected preset and changes the menu title temporarily. It doesn't store nor provide access to preset selection info. I needed this feature once, and had to subclass the operator myself to get it.

Yes, you can only check specific values modified by the preset's script file.